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Re: What is zero divided by zero anyway?

by moxliukas (Curate)
on Oct 05, 2002 at 21:43 UTC ( #203094=note: print w/replies, xml ) Need Help??

in reply to What is zero divided by zero anyway?

I have always thought that there are three possible answers to the question what is 0 / 0:

  • zero, since zero divided by anything is still zero;
  • infinity, since anything divided by zero is infinity;
  • one, since anything divided by itself is one.

Of course my thinking can be very wrong as zero is not just anything -- it is a special case in itself. 0 / 0 may be equal to zero, one and infinity at the same time, but it is probably easier to say that it is undefined. Or even Mu.

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Re^2: What is zero divided by zero anyway?
by Aristotle (Chancellor) on Oct 06, 2002 at 10:39 UTC

    Yes, the answer is that the result of x/0 (including x=0) is every possible result at once. That is because x*0 is zero for any x. With x*a for any a != 0 the result set is exactly as large as the definition set (I hope these are the correct English terms). But for a = 0, the result set has only a single value, 0 itself.

    x*a maps every x to one distinct y, except for a=0, so you can reverse it. But for a=0, it maps every x to the same y (that is, to 0), so by knowing a=0 and y=0 you still cannot tell which out of an infinite number of possible values for x led to this result.

    Makeshifts last the longest.

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[stevieb]: ...has honed in my skills of recognizing sound
[stevieb]: All of the early members are coming out of the woodwork today :) Hey, planetscape
[Corion]: This cover version had so much promise but the singing is underwhelming :-/
[stevieb]: erix Thanks! I dislike remakes of songs usually, but my favourite remix of guitar/weeps is Jeff Healey. I'll take a listen to yours
[planetscape]: hi stevieb!
[stonecolddevin]: also hi Corion
[Corion]: stevieb: Yeah, but I don't follow guitar players enough... I never got Prince and I don't think I could recognize his play style. I can recognize Santana and Nile Rodgers, but that's about it, and not really deep knowledge I think ;)
[stevieb]: Jeff Healey cut of My guitar gently weeps
[stonecolddevin]: you don't recognize Prince. Prince tells you it's him.
[erix]: Alvin Lee (Ten Years After) played a jazzguitar ("Big Red"), a good warm sound

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